I'm pretty certain that TP Link would win handily in a one-on-one duel. He's essentially got all of WW Link's tricks minus the Hurricane spin plus the Mortal Draw, Jump Strike, Ending Blow, and Great Spin. His normal moves are kind of "locked in" in the sense that he's pretty much standing in one place while moving his sword around, but that's usually a boon in, again, one on one matches. His style is much more precise than WW.
However, we're not talking about a duel here. In this scenario, TP and WW are not fighting one-on-one, but rather a huge brawl between like ten Links. Fire arrows, boomerangs, and hookshots are bound to be flying everywhere, especially from the 2D Links with pathetic "slash in front" moves. In this situation, TP Link's precise style is going to be of little help to him, as he'll largely be staying in one place whenever he tries to press his formidable offense. Although only the 3D Links (and MC) really have considerable talent with the sword, TP Link's (and OoT/MM Link's) styles are similarly static. WW Link is the primary exception to this rule. Even his basic sword techniques are moving him over the ground his enemy loses, making it very easy for him to attack without getting "stuck" in a duel-like combat. While other Links normally have to be stationary to attack effectively, WW Link can be nimble while attacking, which provides him with the unique ability among the Links to not fear pressing an assault. It also makes it harder for the Links who rely on projectiles and such to get a bead on him- nothing can distract him or keep him still long enough to get off a good arrow or boomerang.
In my mind, WW Link is going to dominate the first half of the combat. While other Links are easy targets while readying themselves to attack, WW Link is going to be hit much less often. Meanwhile, TP Link, who possesses the Back Slice and Helm Splitter, is similarly going to be rather effective in this regard- in fact, while WW is clearly the king of offensive mobility, TP still beats out many of the others. To be honest, the final outcome is going to depend entirely on either 2D gimmicks (how effective are Bombos, Ether, Quake, Thunder, Din's Fire, or other area magics?) or how much TP gets beat up. If WW Link evades enough and TP takes too many bad hits, the health difference is likely to make the endgame odds even or better for WW.
So let's sum: WW Link has superior offensive mobility and is likely to come out of the first round (that is, until most of the untalented 2D Links are knocked out) without much damage, making the final duels by default in his favor.
TP Link has the most raw power and the second best mobility. He's also got some seriously powerful Hidden Skills such as the Great Spin and Mortal Draw that make him a serious threat in one-on-one combat.
OoT/MM Link and his adult counterpart are remarkably similar. OoT, MC, WW, and TP are the only Links with a jump attack, making up for a lack of real offensive mobility. He's also got Nayru's Love and Din's Fire, two area spells with decent effects. Din's Fire leaves him open, though, and Nayru's Love is no substitute for Magic Armor. However, the defense upgrade from the Great Fairy makes him fairly durable.
LoZ/AoL Link doesn't have much in his original game other than the recorder, which summons a tornado, but WW Link can do that too, I guess. However, in AoL, he gains some real game-breakers. Thunder is a way-powerful nuke spell that hits everything nearby, but it doesn't immediately kill bosses and thus isn't likely to have much of an impact on the average Link's crazy huge endurance meter. Life is severely hampered by the fact that it draws on his limited magic pool, as are most of his spells.
LttP/LA Link can get himself some really overpowered swords, but when your abilities are limited to "slash in front of you" and "spin around", it's less helpful. He does, however, have a ton of crazy trump card items, such as Bombos, Ether, Quake, and the Cane of Byrna. A large magic meter for these spells is also helpful, unlike AoL's sharply limited magic. It kind of depends on how his nuke spells stack up against the Link health meter, but their effectiveness on bosses is an indicator that says they might not be as powerful as they seem.
I haven't played the Oracles yet, so I'll leave them alone for now. However, I'm pretty certain they don't have much special in the way of weaponry- just the usual hookshots, arrows, bombs, and stuff. If anyone has input on this, that'd be great.
I haven't played MC, either, but I've seen LPs. He's got a surprising arsenal of sword moves, and although his basic abilities are limited to "slash and slash again", his skills allow him the kind of versatility the 3D Links tend to have. The Jump attack is the biggest selling point, actually- it gives him the much-needed offensive mobility compared to other 2D Links that he's likely to be one of the few 2D survivors of the initial round.
Finally, we've got FS/A. The main point here is that there's four of them. Problem is, they can only carry one weapon at once, and so even with their advantage of numbers, it's really just four extremely weak 2D Links. I doubt they'd present much of a problem for anyone unless they ganged up, but they're not likely to come out of the first round without their numbers too diminished to be effective.